A graph is called supermagic if it admits a labelling of the edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce a new construction of supermagic graphs using the special structure of their subgraphs. The supermagic complements of some bipartite grap...

We consider two innnite games, played on a countable graph G given with an integer vertex labelling. One player seeks to construct a ray (a one-way innnite path) in G, so that the ray's labels dominate or elude domination by an integer sequence being constructed by another player. For each game, we give a structural characterization of the graphs on which one player or the other can win, provid...

Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V (G) to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum (under the operation of A) of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V (G) to A such that the weights of ...

In this paper we introduce a new graph based bidding language for combinatorial auctions. In our language, each bidder submits to the arbitrator a generalized flow network (netbid) representing her bids. The interpretation of the winner determination problem as an aggregation of individual preferences represented as flowbids allows building an aggregate netbid for its representation. Labelling ...

Given an acyclic directed graph and two distinct nodes s and t, we consider the problem of finding k disjoint paths from s to t satisfying some objective. We consider four objectives, MinMax, Balanced, MinSum-MinMin, and MinSum-MinMax. We use the algorithm by Perl-Shiloach and labelling and scaling techniques to devise an FPTAS for the first three objectives. For the forth one, we propose a gen...

A labeling of edges and vertices a simple graph \(G(V,E)\) by mapping \(\Lambda :V\left( G \right) \cup E\left( \to \left\{ { 1,2,3, \ldots ,\Psi } \right\}\) provided that any two pair have distinct weights is called an edge irregular total \(\Psi\)-labeling. If \(\Psi\) minimum \(G\) admits -labelling, then the irregularity strength (TEIS) denoted \(\mathrm{tes}\left(G\right).\) In this paper...

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Random...

A mapping from the vertex set of a graph G = (V,E) into an interval of integers {0, . . . , k} is an L(2, 1)-labelling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbour are mapped onto distinct integers. It is known that for any fixed k ≥ 4, deciding the existence of such a labelling is an NP-complete p...